QM + GR = black holes cannot exist

[Farsight]

Thanks tashja. I have to say the above answer is wrong. I can only presume it was something off-the-cuff for the wrong audience. Spacetime curvature, not spatial curvature, is associated with the tidal force, not the force of gravity. Tidal force relates to the second derivative of potential, and it isn't detectable in the room you're in. The force of gravity relates to the first derivative of potential, and there's no problem detecting your pencil falling down. See this black hole article for something about the "spacetime tilt" we've spoken about previously. In flat spacetime all the light cones are vertical, in curved spacetime they tip over towards the star. They're more tipped over closer to the star where the force of gravity is higher. The force of gravity relates to the degree of tipping or tilt. You need spacetime curvature to get this tilt, but the pencil falls down because of the tilt, not the curvature. The steeper the tilt, the greater the acceleration.

PS: At least he didn't say it's because space is falling inwards towards the centre of the Earth.

Nimbus: my previous comments stand. Everything you're quoting dates from 2006.

 

[wellwisher]

Acceleration has the units of d/t/t (d t t) whereas space-time is d t. Where does the extra unit of time come from, since acceleration and space-time don't have the same units, but differ by time? Does gravity add time to space-time to get acceleration?

A curved path adds an acceleration. Again this is consistent with adding an extra time unit to space-time to get d t t units.

 

[Dr_Toad]

Trick or Treat: Two comments above by people who don't know maths or physics. At least wellwisher admits it.

 

[PhysBang]

Thanks tashja. I have to say the above answer is wrong. I can only presume it was something off-the-cuff for the wrong audience. Spacetime curvature, not spatial curvature, is associated with the tidal force, not the force of gravity. Tidal force relates to the second derivative of potential, and it isn't detectable in the room you're in. The force of gravity relates to the first derivative of potential, and there's no problem detecting your pencil falling down.

OK, you talk the talk, let's see you walk the walk: do an example of a pencil falling and show us where the derivatives come in to play. And show us where the inhomogeneous space comes in.

Then we can see if your "interpretation" of gravity makes any sense.

See this black hole article for something about the "spacetime tilt" we've spoken about previously. In flat spacetime all the light cones are vertical, in curved spacetime they tip over towards the star. They're more tipped over closer to the star where the force of gravity is higher. The force of gravity relates to the degree of tipping or tilt. You need spacetime curvature to get this tilt, but the pencil falls down because of the tilt, not the curvature. The steeper the tilt, the greater the acceleration.

This is yet another "own goals" from your citations, Farsight. When you first intorduced your idea of "spacetime tilt", you used it as the cause of gravity that was not curved spacetime. Like in the citation you used there, the first use of "spacetime tilt" in that article is, "The curvature of spacetime, then, will be depicted by the tilting of these lightcones." So, your own citation, again, says that gravity is curved spacetime.

You could, perhaps, clear up your position if you walk us through the fall of a pencil with some actual details (that is, mass and velocity values and equations).

PS: At least he didn't say it's because space is falling inwards towards the centre of the Earth.

Yes, he did. You just can't understand the answer.

Nimbus: my previous comments stand. Everything you're quoting dates from 2006.

Yes, someone who knows the physics might have been hit on the head or had a stroke and forgotten major points in the intervening eight years. However, this would make them a poor choice for an argument from authority.

 

[wellwisher]

Trick or Treat: Two comments above by people who don't know maths or physics. At least wellwisher admits it.

I understand physics, although my math is not what it used to be. I don't agree with math conclusions that are not conceptually consistent with basic observations. I look for better conceptual models behind the math and not math tricks to avoid dealing with conceptual flaws.

I am/was engineer and a simple dimensional analysis is a very useful tool to make sure a complex conceptual model of a process is sound; before you build. Space-time has the units of distance (space) and time, while acceleration, such as via force, is distance (space), time and time. Space-time is consistent with velocity (distance and time). Space-time is missing an extra unit of time, compared to acceleration and curved paths. I gave you a treat (more time) to explain gravity.

My guess is since gravity is caused by mass, mass is adding the extra time to local space-time. Space-time, by itself, does not contain the extra time unit that is given expression via curved paths and acceleration. Mass, via the extra unit of time, allows accelerations due to the gravitational force and as well curved paths due to the imaginary centrifugal force, within space-time.

As I have shown in other topics, gravity generates pressure, which causes phases changes within matter. The solid iron of the earth's core at 6000C, is due to pressure, since on the surface this same iron at 6000C would be in the gas phase. This is not due to space-time or else high velocity would cause material changes due to changes within space-time; space ships would implode. This is not assumed by anyone. Pressure is not a space-time induction. Pressure is cased by the extra time within mass, since pressure is force/area with force an acceleration that needs d,t,t or an extra unit of time.

Time potential connects gravity to acceleration, pressure and curve paths within space-time, with pressure the means by which all the forces become connected, via systematic phase changes, as function of pressure. This in turn, is all connected to extra time potential in space-time.

 

[PhysBang]

As I have shown in other topics, gravity generates pressure,

I think it's far too grandiose for you to claim to have shown this, since it has been in every textbook for at least two centuries.

So again I ask you, do you think that there i pressure in Newtonian universal gravity?

 

[nimbus]

Sorry folks, I just noticed some of the pages I referred to in my post #603 are restricted.
So, here's pages 504, 506, 507, and 508...

Click on to view and use the top right diagonal arrow to see better image.
I have underlined some.

 

[PhysBang]

That's some great writing. I'm going to have to see if I can dig up a copy.

Unfortunately, Springer cancelled the "Yellow Sale", at least for the most part, so I'll have to do some hunting.

 

[Beer w/Straw]

I would like to read textbook writing of present day.

So blame me for being angry if not.

 

[brucep]

Acceleration has the units of d/t/t (d t t) whereas space-time is d t. Where does the extra unit of time come from, since acceleration and space-time don't have the same units, but differ by time? Does gravity add time to space-time to get acceleration?

A curved path adds an acceleration. Again this is consistent with adding an extra time unit to space-time to get d t t units.

Meters per second per second. Meters per second is speed and meters per second per second is acceleration. Can't know to much about physics if dimensional analysis is beyond your ability to understand. A curved path doesn't contribute to the acceleration. Accleration along a curved path doesn't produce a force that would need to be included in the analysis.

 

[brucep]

You'll be waiting awhile

Mainstream has NO idea of gravity , other than some abstract mathematical representation , of which has no basis in reality

I'd call you intellectually dishonest but you clearly have no intellect to call dishonest. You proof this every time you post in this forum. You're a poster child for the right wing sycophant.

 

[brucep]

Farsight, you often like to cite Don Koks as agreeing with you, but he doesn't.

See the following from Don koks book ‘Explorations in Mathematical-Physics: The Concepts behind an Elegant Language’.

On page 501, he describes how using Schwarzschild spacetime coordinates brings about the slowing of a clock to zero at the horizon. He then asks…

He goes on to say…

On page 506, Don Koks goes on…

To this end, Don Koks continues with a couple of pages of equations to end on page 508 with…
My underline in above quotes.
Farsight, he doesn't agree with you about time stopping for all frames at the event horizon, because he says 'we know for certain that spacetime is perfectly well behaved there'. And Mr Koks reckons the Kruskal-Szekeres are 'a good set of coordinates'.

A note to some…r = 0 is the singularity at the centre of a classical black hole and r = 2M is the event horizon.
The Schwarzschild spacetime coordinates mentioned on page 501 are those used by the distant observer.
-----------
About the link …You will land on page 499, a restricted yellow page, just scroll or click the page turner to move on to page 501. Book link

Very informative posts nimbus. Thanks.

 

[brucep]

Bah, you never do any physics, or point to any flaws in the physics I provide, because you're just a naysayer troll intent on spoiling discussions and trashing threads. It's back on ignore for you.


He agrees with me about the speed of light varying with position, like Einstein said and optical clocks demonstrate.

The book dates from 2006. If you were to ask him now, maybe he'd have a different view. Tell you what, why don't you email him? Refer him to page 501 where he says light slows to zero as it approaches r=2M, and tell him that I said Kruskal-Szekeres coordinates contain a schoolboy error: a stopped observer allegedly sees a stopped clock ticking normally. No he doesn't. The clock is stopped, and he's stopped too. He sees nothing.

View attachment 42

Why would he change his mind about stuff that's been understood for a century. You're the one who doesn't understand what you're discussing. You can't even understand why you're analysis is full of crap as evidences by your never ending bullshit analysis.

 

[nimbus]

But it's academic anyway, the book dates from 2009, and it isn't actively on sale. There a few used copies with prices up to £101.89, but no new copies.

Farsight, given that you (john Duffield) are listed as company director of the publishing company (Corella ltd) which published your own book, do you think the book is worth another print run?

Asking me to e-mail Don Koks is so lame.
To use your words 'tell you what', why don't you show us where Mr Koks gets it wrong in his equations on pages 506 t0 508, ending with the statement on page 508...

So with this time-space swap incorporated, the normalised Riemann components don’t diverge at r = 2M, and we know for certain that spacetime is perfectly well behaved there.

 

[tashja]

I contacted Prof. Koks and provided him with a link to the thread. Here's his reply:

You're standing on a gedanken planet holding a laser pointer straight up. The light doesn't curve round, or slow down as it ascends, or fall down. It goes straight up. Now I wave my magic wand and make the planet denser and more massive. The light still doesn't curve round, or slow down as it ascends, or fall down. I make the planet even denser and more massive. The light still doesn't curve round, or slow down as it ascends, or fall down. I make the planet even denser and more massive, and take it to the limit such that it's a black hole. At no point did the light ever curve round, or slow down as it ascends, or fall down. So why doesn't the light get out?

Prof. Koks:

First, any experiment that "makes" a black hole--especially viewed from below the horizon--is fraught with difficulty. Inside a Schwarzschild black hole space and time swap roles, and our intuition of how to construct a physical argument becomes suspect to say the least. One cannot make a Schwarzschild black hole (which I presume is the type you are discussing). It's a solution to Einstein's equations for a very very simple universe: one that contains at most one point mass, and which never changes; it has always existed and will always continue to exist, by construction. It turns out that this solution also applies outside a spherically symmetric non-point mass. Regardless of that, such a universe is very artificial, and the predictions that arise from analysing Schwarzschild spacetime don't necessarily apply to more realistic universes. Because the ideas that go into the Schwarzschild case presuppose the universe to exist forever unchanged, one must be on guard for odd predictions that involve eternity in some uncomfortable way, or that clash with intuition. If a real black hole is ever discovered for certain, it will presumably be a much more complex object than the Schwarzschild case, and probably a lot more complex than even the rotating charged black hole solution to Einstein's equations.

Your black-hole discussion seems to be have started with the speed of light and then evolved into a discussion of which coordinates are good and which are bad. I suggest that if black-hole discussions are creating arguments then you should return to special relativity to see what that will tell you, because at least the literature on special relativity tends to be easier to read and understand, and probably will be agreed on more widely. So I suggest looking to the Equivalence Principle. The principle says that the room you are sitting in right now is very well approximated as a "uniformly accelerated frame" in the absence of gravity. This frame can be analysed using special relativity only, yet still embodies the essentials of what happens when gravity and no acceleration is present. So it serves as a walk-before-you-can-run test bed for what happens outside a black hole at least, and that's the first thing to be considered.

The uniformly accelerated frame is not trying to be "real" gravity. Real gravity is due to masses, and its signature is tidal forces, and these tidal forces don't exist in an accelerated frame. But that's okay: by holding to the Equivalence Principle, whatever we say about a room-sized accelerating rocket ship will apply very accurately to a real room on Earth. If it didn't, there would be no Equivalence Principle.

Although the uniformly accelerated frame can be found mentioned in books under the name of "Rindler space", any real analysis of it is surprisingly hard to find. Even when it is discussed, you'd be excused for thinking that it is some abstract thing of no relevance that may or may not exist in a galaxy far, far away, rather than a very accurate model of the relativity of the room you are sitting in right now. And let's face it, while books spend a lot of time analysing inertial frames due to those frames' importance to relativity, all of us (barring a few astronauts) spend all of our lives in what is, to a high approximation, a uniformly accelerated frame. So it might be a good idea to know a whole lot about such a frame. Unfortunately, the study of such frames is not considered chic enough by many researchers, whose continued academic existence demands that they publish in general relativity and not special relativity. As a result, I think that such frames are seldom given the prominence they deserve. I do discuss them extensively in my book.

Constructing a uniformly accelerated frame is all about constructing a set of coordinates that allows the observers who comprise the frame to agree on simultaneity, what their clocks read, and what the distances are between them. Their clocks all read the same time and the distances between them are fixed: they form a rigid lattice. This is the set of coordinates you want to use if you are to have a useful discussion with someone else in your (accelerated) frame, because then you can all understand the measurements taken and when they were taken. It's by no means obvious that it's possible even to construct such a set of coordinates for a uniformly accelerated frame, but it can actually be done. I won't do that here; I'll discuss the frame a little more qualitatively instead.

Let's use such an accelerated frame to answer the question of whether it's possible even in special relativity for light to travel slower or faster than the standard vacuum inertial value 3 x 10^8 m/s, which I'll denote c from here on. Begin with the all-important topic of the relativity of simultaneity, for which you can find the expression "vL/c^2" in most textbooks that discuss the fundamentals of special relativity. This quantity is the amount of time by which the clock on the tail of a train reads ahead of the driver's clock when the train has rest length L, approaches us at velocity v (positive for approach, negative for recession), and whose clocks are synchronised in its rest frame. Suppose the train is at rest and extends from here to the Andromeda galaxy, so that its driver is right next to us and its tail sits in that galaxy, which we'll suppose isn't moving relative to us. Our standard of simultaneity says that right now on a particular planet in the Andromeda galaxy at the tail of the train, some clock reads zero just as ours reads zero, and that clock clicks at the same rate as ours. Now start moving and walk towards the galaxy at 1 m/s. Suddenly the space between here and Andromeda has become like the train mentioned above: that "train" is approaching us at v = 1 m/s with L = 2 million light-years, so that the clock on that particular planet has suddenly jumped ahead of our clock by vL/c^2 = about 2 days. Once we stop accelerating and maintain 1 m/s, the distant clock will run slightly slowly compared to ours (by time dilation), but in the arbitrarily short period of time during which we accelerated, it jumped 2 days ahead.

Imagine that two planets in that galaxy are 2 light-days apart, and one sends a pulse of light to the other. During the period that we accelerated and clocks in Andromeda jumped 2 days ahead of us, that light pulse travelled from one planet to the other. But we can accelerate however quickly we like, so we'll conclude that during our brief period of acceleration, the light passing between those two planets travelled much much faster than c. So while you accelerate towards Andromeda, both light and clocks (i.e. the flow of time itself) speed up in Andromeda--but only while you accelerate.

None of the preceding discussion actually requires large distances; it's just easier to visualise if we use such large distances. So now transfer that discussion to a rocket you are sitting in, far from any gravity and uniformly accelerated, meaning you feel a constant weight pulling you to the floor. "Above" you (in the direction of your acceleration), time speeds up and light travels faster than c, arbitrarily faster the higher up you want to consider. Now use the Equivalence Principle to infer that in the room you are sitting in right now on Earth, where real gravity is present and you aren't really accelerating (we'll neglect Earth's rotation!), light and time must behave in the same way to a high approximation: light speeds up as it ascends from floor to ceiling (it doesn't slow down, as apparently quoted on your discussion site), and it slows down as it descends from ceiling to floor; it's not like a ball that slows on the way up and goes faster on the way down. Light travels faster near the ceiling than near the floor. But where -you- are, you always measure it to travel at c, because no matter where you place yourself, the mechanism that runs the clock you're using to measure the light's speed will speed up or slow down precisely in step with what the light is doing. If you're fixed to the ceiling, you measure light that is right next to you to travel at c. And if you're fixed to the floor, you measure light that is right next to you to travel at c. But if you are on the floor, you maintain that light travels faster than c near the ceiling. And if you're on the ceiling, you maintain that light travels slower than c near the floor.

You can also infer that as a distant wavefront travels transversely to your "up" direction, the more distant parts of it will be travelling faster than the nearer parts. So, just as light bends when it enters glass at an angle, you won't be surprised to see the distant light bend toward you. And, of course, bending light is something you'll find in textbooks that illustrate the Equivalence Principle with a picture of a guy in an elevator encountering a beam of light.

(Continued below)

 

[tashja]

Next step: again in the zero-gravity accelerated frame, as you accelerate toward Andromeda, ask what happens in the direction opposite to Andromeda. Think of another train behind you if you prefer, but now "v" has changed sign: the train is receding instead of approaching. So your changing standard of simultaneity makes clock readings behind you jump backwards, even though the "train clocks" themselves are still "timing forwards" as far as they are concerned. The clocks immediately behind you will appear almost normal, but at some critical distance further back, the amount by which your new standard of simultaneity makes them seem to jump back just balances the amount by which they have timed forwards, and the result is that, as far as your standard of simultaneity is concerned, they have stopped. This is all about -your- standard of simultaneity. The clocks themselves don't know anything about what you're doing of course; they just continue to do what they were built to do. It turns out that if you accelerate with some value "a" (meaning you feel a constant acceleration of "a"--and that means your world line is actually a hyperbola on a spacetime diagram on which inertial observers follow straight world lines), then this critical distance behind you at which you maintain that time and light have stopped is c^2/a. So if you accelerate at one Earth gravity, that distance is about 0.97 light-years, which is near enough to one light-year to make a nice rule of thumb. The more strongly you accelerate, the closer the horizon will be to you. If you stop accelerating, the horizon moves off to be infinitely far away.

So imagine again that the room in which you're sitting is an accelerating rocket far from gravity, and your weight is due to its acceleration upwards. Your 1-g acceleration means you infer that light and time flow faster above you and slower below you. About one light-year below you is a plane parallel to the floor on which light and time slow to a stop. It's a horizon. Below that plane time flows backwards, but you can never receive a signal from below that plane--a fact that you can prove easily with a quick sketch on the spacetime diagram of an inertial observer, where you'll notice that you'll forever outrun a light signal that was sent to chase you from that far away, even though an inertial observer says that the light is travelling (at c) faster than you are. So you'll never see any weird breakage of causality occurring beyond the horizon.

Saying that light and time have stopped on this horizon is a consequence of your changing standard of simultaneity as you accelerate. Anyone sitting on or beyond the horizon just continues life as usual; they can't be influenced by your state of motion. Although you maintain that they have stopped evolving, they themselves notice nothing unusual. In that sense, what we say about the flow of time and the speed of light is all about the coordinates that we have used to describe the world of our accelerated frame. But those coordinates are not silly and arbitrary, because they reflect the fact that we can build our accelerated frame by using the standard mechanism of making measurements in special relativity: we construct a rigid lattice of observers whose clocks always agree with ours, and who don't move relative to us. This construction is precisely what a uniformly accelerated frame is, and it's by no means obvious that it's possible to do: for example, in an inertial frame, the accelerations of those other observers will differ from our own acceleration--even though they remain at a fixed distance from us. That might sound odd, and to see why it's true, you have to follow the special-relativistic ideas of simultaneity, timing, and length very carefully. (And yes, see my book for the details.) So although this changing standard of simultaneity might be referred to by some as just some kind of coordinate artifact, we shouldn't trivialise the use of such coordinates. They are what our world is built on.

This changing standard of simultaneity of an accelerating observer is the real kernel behind resolving the Twin Paradox. Every book discussing the Twin Paradox that I've ever seen (apart from my own) seems to want to simplify things by having the space traveller maintain constant speed on both the outbound and inbound leg, necessitating an infinitesimal period of infinite acceleration at the start of the return trip. And in so doing, these discussions throw the baby out with the bath water by producing an analysis that contains an awkward gap in the timing at the moment the space traveller changes direction. If those analyses were to have the traveller accelerate in a more realistic way, what would result would be a very much more difficult, yet far more complete, analysis of the Twin Paradox that has no weird timing gaps.

You can see that as you go about your daily life, accelerating every which way as you walk around, your standard of simultaneity is see-sawing madly all around you. Playing around with lines of simultaneity on a spacetime diagram and maintaining that time is doing weird things are we accelerate might seem like a departure from good common sense. We must appeal to experiment to keep from straying into an abstract fairy world that has nothing to do with reality. But remember that via the Equivalence Principle, these special-relativistic ideas of changing simultaneity feed into general relativity, and in this day and age we -do- have the luxury of experiments that daily confirm that more advanced theory. If general relativity didn't work, then the GPS satellite system would fail dismally at telling you where you are and what the time is.

Many people maintain that light only ever moves at c. Not so. If you measure the speed of light that is right next to you, you'll always find it to move at c. Light that is not right next to you won't move at c if you're accelerating and using the coordinates that are completely natural to your accelerated frame. But how can you measure its speed if it's not right next to you? You do that through the standard mechanism, mentioned above, of employing a lattice of observers whose clocks always agree with yours, and who don't move relative to you. You then use the measurement of the observer who was right next to the light whose speed you wanted to measure. And that's fine, because that observer in not moving relative to you, and their clock always agrees with yours. That's the standard way that -all- measurements are done in the context of special relativity.

Making observations from an -inertial- frame (and using its coordinates) shows that nothing untoward is happening on the horizon that is present in the -accelerated- frame. So in that respect the inertial frame's coordinates are better for some analyses, even though the accelerated frame is more natural to our description of the world around us. After all, we don't spend our days in free fall. The same is true for describing the spacetime around a Schwarzschild black hole. The analogy of the accelerated frame (with its horizon) is the usual coordinate set--call it Schwarzschild coordinates if you like--that exhibits a horizon. Just as we can replace accelerated-frame coordinates by inertial-frame coordinates to make the horizon go away, so to speak, so too we can replace Schwarzschild coordinates by Kruskal coordinates to make the black-hole horizon go away.

He agrees with me about the speed of light varying with position, like Einstein said and optical clocks demonstrate.
The book dates from 2006. If you were to ask him now, maybe he'd have a
different view. Tell you what, why don't you email him? Refer him to page 501 where he says light slows to zero as it approaches r=2M, and tell him that I said Kruskal-Szekeres coordinates contain a schoolboy error: a stopped observer allegedly sees a stopped clock ticking normally. No he doesn't. The clock is stopped, and he's stopped too. He sees nothing.

And now finally, you can begin to look at statements about Kruskal coordinates, and appreciate that they are useful for showing that observers sitting (however briefly) right on a Schwarzschild horizon find nothing unusual to be happening there, even though we who are distant from that horizon maintain that their clocks have stopped. Analysing events using different coordinates shows that what can be knotty in one set can be just fine in a different set. It's just like choosing coordinates other than latitude/longitude to describe Earth's poles. And that's all just as true in 2014 as it was in 2006.

 

[Farsight]

Good stuff tashja. Thanks for doing that, and thanks Don for putting so much time into the reply.

do you think the book is worth another print run?

No, I've learned a lot since 2009, I'd do a new book. See above, Don Koks still thinks Kruskal-Szekeres coordinates are valid.

 

[nimbus]

Yes, thanks for that Tasha and Don Koks.
Tasha you saved me having to find an e-mail address for don Koks.

Don Koks still thinks Kruskal-Szekeres coordinates are valid.

Farsight, where does that leave your stopped clocks on the event horizon for ALL frames, including the in-faller's?
You said everyones a 'popsicle' on the horizon.
And, you also said something like...you don't see a stopped clock on the horizon because light has stopped there too.

Don Koks from above...

And now finally, you can begin to look at statements about Kruskal coordinates, and appreciate that they are useful for showing that observers sitting (however briefly) right on a Schwarzschild horizon find nothing unusual to be happening there,

Farsight,where does that leave your 'idea' has to what gravity is, since when at the horzion you ' find nothing unusual to be happening there,'.
Mr Koks

'sitting (however briefly) right on a Schwarzschild horizon'

Farsight, why ' however briefly' at the horizon,' has someone fallen in? and will you be mentioning any of this in your next self published book?

 

[Farsight]

Farsight, where does that leave your stopped clocks on the event horizon for ALL frames, including the in-faller's?
You said everyones a 'popsicle' on the horizon. And, you also said something like...you don't see a stopped clock on the horizon because light has stopped there too.

I stand by what I said.

Farsight,where does that leave your 'idea' has to what gravity is, since when at the horizon you ' find nothing unusual to be happening there,'

It isn't my idea, it's the "frozen star" interpretation referred to here. Don Koks doesn't agree with me, such is life.

Farsight, why ' however briefly' at the horizon,' has someone fallen in?

I don't know what you mean, nimbus.

and will you be mentioning any of this in your next self published book?

What next book? I have no current plans. But you know, maybe I should write a paper.

 

[Beer w/Straw]

Explain why a pencil falls.